Quantification of heavy particle segregation in turbulent flows: a Lagrangian approach

The way particles suspended in a turbulent flow are transported and segregated by turbulent structures is crucial in many atmospheric and industrial applications such as powder production and formation and growth of PM10 particulate. In recent years, this phenomenon has been studied from different viewpoints; lately, Osiptsov [1] proposed an alternative approach to quantify particle segregation, later followed by [2] and [3]. This method, referred to as ‘Full Lagrangian approach (FLA)’, evaluates the size of an infinitesimally small volume of particles and its changes in the course of time along each particle trajectory. The rate of deformation of this volume is related to the compressibility of the particle velocity field (e.g. [4]) which is an indicator of particle concentration. This method presents high computational efficiency in comparison with traditional Eulerian methods such as “box-counting”, for which a large number of particles is required to obtain accurate statistics. We decided to exploit FLA in a simple two-dimension synthetic turbulent flow field Direct Numerical Simulations of homogeneous isotropic turbulence, and to compare it with the MEPFV, a method proposed by [5] et al. essentially based on box counting. Preliminary results of the spatially averaged statistics of the rate of deformation are also presented, showing that the presence of singularities increases for large St numbers. In this work, we study the dispersion of identical, rigid and spherical particles in a carrier flow of mass density ρ and kinematic viscosity ν. Particles are assumed to be heavy (i.e. ρp/ρ » 1 where ρp is the particle density) with radii aρ much smaller than the smallest length scale of the flow. Upon neglecting gravity and Brownian effects, the equations of motion are [6]: 1 where xp and v are the position and velocity of the particle respectively, and u = u(xp, t) denotes the velocity of the carrier flow at the position of the particle. All variables have been made dimensionless by a typical time scale ד and a typical velocity scale U. The parameter is the Stokes number, which represents the ratio between the inertia driving the particle and the viscous damping action of the fluid.